This note is concerned with the study of temporal development in several indices reflecting clustering effects in multilevel designs that are frequently utilized in educational and behavioral research. A latent variable method-based approach is outlined, which can be used to point and interval estimate the growth or decline in important functions…

Cluster randomized trials (CRTs) are commonly used to evaluate the causal effects of educational interventions, where the entire clusters (e.g., schools) are randomly assigned to treatment or control conditions. This study introduces statistical methods for designing and analyzing two-level (e.g., students nested within schools) and three-level…

In this article, we present a two-stage estimation approach applied to multilevel latent class analysis (LCA) with covariates. We separate the estimation of the measurement and structural model. This makes the extension of the structural model computationally efficient. We investigate the robustness against misspecifications of the proposed…

Multivariate analysis of variance (MANOVA) is widely used to test the null hypothesis of equal multivariate means across 2 or more groups. MANOVA rests upon an assumption that error terms are independent of one another, which can be violated if individuals are clustered or nested within groups, such as schools. Ignoring such nesting can result in…

Hierarchical data is often observed in education data. Analyzing such data with Multilevel Modeling becomes crucial to understanding the relationship at the individual and group levels. However, one of the most significant problems with this kind of data is small sample sizes and very low Intraclass Correlations. The multivariate Latent Covariate…

Cluster memberships associated with the mediation effect are often changed due to the temporal distance between the cause-and-effect variables in longitudinal data. Nevertheless, current practices in multilevel mediation analysis mostly assume a purely hierarchical data structure. A Monte Carlo simulation study is conducted to examine the…

Mixture modeling is a latent variable (i.e., a variable that cannot be measured directly) approach to quantitatively represent unobserved subpopulations within an overall population. It includes a range of cross-sectional (such as latent class [LCA] or latent profile analysis) and longitudinal (such as latent transition analysis) analyses and is…

Within-cluster variance homogeneity is one of the key assumptions of multilevel models; however, assuming a constant (i.e. equal) within-cluster variance may not be realistic. Moreover, existent within-cluster variance heterogeneity should be regarded as a source of additional information rather than a violation of a model assumption. This study…

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other…

Background: Counts are familiar outcomes in education research settings, including those involving tests of interventions. Clustered data commonly occur in education research studies, given that data are often collected from students within classrooms or schools. There is a wide array of distributions and models that can be used for clustered…

Multilevel latent class analysis (MLCA) has been increasingly used to investigate unobserved population heterogeneity while taking into account data dependency. Nonparametric MLCA has gained much popularity due to the advantage of classifying both individuals and clusters into latent classes. This study demonstrated the need to relax the…

The year 2022 is the 20th anniversary of Joseph Schafer and John Graham's paper titled "Missing data: Our view of the state of the art," currently the most highly cited paper in the history of "Psychological Methods." Much has changed since 2002, as missing data methodologies have continually evolved and improved; the range of…

Multilevel modeling (MLM) is a statistical technique for analyzing clustered data. Despite its long history, the technique and accompanying computer programs are rapidly evolving. Given the complexity of multilevel models, it is crucial for researchers to provide complete and transparent descriptions of the data, statistical analyses, and results.…

When selecting a multilevel model to fit to a dataset, it is important to choose both a model that best matches characteristics of the data's structure, but also to include the appropriate fixed and random effects parameters. For example, when researchers analyze clustered data (e.g., students nested within schools), the multilevel model can be…